The decibel is a unit of measurement that gives the ratio of the power of one signal relative to another. The formula for the decibel is dB = 10 * log_10(P1 / P2) where P1 and P2 are power measurements. The reason it is called a decibel is because it is 10 bels. One bel would be log_10(P1/P2).

The important thing to understand is that the decibel is a RATIO of powers. A dB is meaningless without a reference power. So if someone says "that signal is 86 dB" that is a meaningless number as it has no reference.

Decibels are convenient because they convert logarithmic perception to a linear scale. Human hearing, for example, is logarithmic. Many other natural phenomena are logarithmic which means that the phenomena exists in the "multiplication domain" as opposed to the "addition domain". For example, human vision is logarithmic. We perceive light such that the light must double for it to appear twice as bright. If we were to plot that we would have an exponential curve of light intensity vs. perceived brightness. If we take the logarithm of the intensity instead we get a straight line. This is why cameras use f-stops which are a base-2 logarithm.

So, back to reference levels. There are many reference levels used in dB: dBm, dBu, dBV, dB re. kPa, etc. dBm refers to the power referenced to one milliwatt. If the measured power is, say, 100 mW then that would be 10 * log10(100/1) = 10 * log10(100) = 20 dBm. dBV is a voltage ratio and not really a true dB but, regardless, is still commonly used. The formula for dBV is 20 * log10(V1/V2) since we need to square the voltage to get the power.

In audio a common unit is dBu. dBu is the power relative to the voltage into a 600 ohm resistor that is dissipating 1 mW. This is roughly 0.77 volts. Back in the early days of telecom 600 ohms was the standard termination impedance, hence the dBu. Most pro audio gear runs at +4 dBu. What does that mean? 0 dBu is 0.77 volts so +4 dBu would be 4 dB greater, or about 1.22 volts. To go from dB to volts the formula is 10^(dB/20).

Consumer audio gear usually runs at -10dBV, or roughly 0.32 volts.

When recording your goal is to get your signal level near the nominal signal level of the equipment being used. This ensures the best S/N ratio. Many recording consoles use VU meters which are calibrated such that "0 dB" is +4 dBu. The goal is to get your signal level around 0 dB.

Well-designed gear has some amount of "headroom". Headroom is the difference between the maximum signal level and the nominal signal level. For example, the Axe-Fx II has a maximum signal level of +18 dBu. If operating at +4 dBu nominal this gives 14 dB of headroom which means that any signal peaks can be over four times higher.

In digital gear we encounter the dBFS, which is dB relative to full-scale. Full-scale is a term that indicates the maximum signal level into or out of an A/D or D/A converter, respectively. With digital converters the best performance is achieved by operating the converter such that the nominal signal level is close to full-scale. The exact voltage is unknown and irrelevant. Most digital gear will have indicators that measure the levels relative to the converter's full-scale value. For example, the input meters on the Axe-Fx indicate the input signal relative to the A/D converter's full-scale value. The "tickle the red" advice aims to operate the A/D converter near its full-scale value as the red LEDs light at 6 dB below full-scale, or -6 dBFS.

The important thing to understand is that the decibel is a RATIO of powers. A dB is meaningless without a reference power. So if someone says "that signal is 86 dB" that is a meaningless number as it has no reference.

Decibels are convenient because they convert logarithmic perception to a linear scale. Human hearing, for example, is logarithmic. Many other natural phenomena are logarithmic which means that the phenomena exists in the "multiplication domain" as opposed to the "addition domain". For example, human vision is logarithmic. We perceive light such that the light must double for it to appear twice as bright. If we were to plot that we would have an exponential curve of light intensity vs. perceived brightness. If we take the logarithm of the intensity instead we get a straight line. This is why cameras use f-stops which are a base-2 logarithm.

So, back to reference levels. There are many reference levels used in dB: dBm, dBu, dBV, dB re. kPa, etc. dBm refers to the power referenced to one milliwatt. If the measured power is, say, 100 mW then that would be 10 * log10(100/1) = 10 * log10(100) = 20 dBm. dBV is a voltage ratio and not really a true dB but, regardless, is still commonly used. The formula for dBV is 20 * log10(V1/V2) since we need to square the voltage to get the power.

In audio a common unit is dBu. dBu is the power relative to the voltage into a 600 ohm resistor that is dissipating 1 mW. This is roughly 0.77 volts. Back in the early days of telecom 600 ohms was the standard termination impedance, hence the dBu. Most pro audio gear runs at +4 dBu. What does that mean? 0 dBu is 0.77 volts so +4 dBu would be 4 dB greater, or about 1.22 volts. To go from dB to volts the formula is 10^(dB/20).

Consumer audio gear usually runs at -10dBV, or roughly 0.32 volts.

When recording your goal is to get your signal level near the nominal signal level of the equipment being used. This ensures the best S/N ratio. Many recording consoles use VU meters which are calibrated such that "0 dB" is +4 dBu. The goal is to get your signal level around 0 dB.

Well-designed gear has some amount of "headroom". Headroom is the difference between the maximum signal level and the nominal signal level. For example, the Axe-Fx II has a maximum signal level of +18 dBu. If operating at +4 dBu nominal this gives 14 dB of headroom which means that any signal peaks can be over four times higher.

In digital gear we encounter the dBFS, which is dB relative to full-scale. Full-scale is a term that indicates the maximum signal level into or out of an A/D or D/A converter, respectively. With digital converters the best performance is achieved by operating the converter such that the nominal signal level is close to full-scale. The exact voltage is unknown and irrelevant. Most digital gear will have indicators that measure the levels relative to the converter's full-scale value. For example, the input meters on the Axe-Fx indicate the input signal relative to the A/D converter's full-scale value. The "tickle the red" advice aims to operate the A/D converter near its full-scale value as the red LEDs light at 6 dB below full-scale, or -6 dBFS.

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